Beginning in 2007, the present PETRA storage ring at DESY will be reconstructed towards a dedicated third generation light source operating at 6 GeV. An emittance down to 1 nmrad can be achieved by means of damping wigglers. We propose a compact permanent magnet wiggler with fixed gap which will be installed in the long straight sections of PETRA. The paper discusses the magnetic design, field distribution, and optical properties. A damping integral I_D ～ 1.25 T~2m per meter wiggler will be reached. The totally required wiggler length of about 80 m will be split into 5 m long segments, each followed by an absorber. The development of these damping wigglers will have a strong spin-off for the ones planned in the damping rings of the TESLA linear collider.
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